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Find the equation of the line given the following points (0,0) and (1,4). Calculate the gradient.

Mathematics

ScanSolve AI Answer

Answer

4

y=4xy = 4x

Step-by-step solution

2 steps

Huu hapa ni ufumbuzi wa swali lako:

Tunapewa pointi mbili: $(0,0)$ na $(1,4)$. Tunahitaji kutafuta gradient na mlinganyo wa mstari.

  1. Kokotoa gradient (mteremko) wa mstari.

    Fomula ya gradient mm ni:

    m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

    Tumia pointi (x1,y1)=(0,0)(x_1, y_1) = (0,0) na (x2,y2)=(1,4)(x_2, y_2) = (1,4).

    m=4−01−0m = \frac{4 - 0}{1 - 0} m=41m = \frac{4}{1} m=4m = 4

    Gradient ni 4\boxed{4}.

  2. Tafuta mlinganyo wa mstari.

    Tunatumia fomula ya mlinganyo wa mstari y−y1=m(x−x1)y - y_1 = m(x - x_1).
    Tumia gradient m=4m=4 na pointi (x1,y1)=(0,0)(x_1, y_1) = (0,0).

    y−0=4(x−0)y - 0 = 4(x - 0) y=4xy = 4x

    Mlinganyo wa mstari ni y=4x\boxed{y = 4x}.

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